Error estimates for barycentric finite volumes combined with nonconforming finite elements applied to nonlinear convection-diffusion problems
Applications of Mathematics, Tome 47 (2002) no. 4, pp. 301-340.

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The subject of the paper is the derivation of error estimates for the combined finite volume-finite element method used for the numerical solution of nonstationary nonlinear convection-diffusion problems. Here we analyze the combination of barycentric finite volumes associated with sides of triangulation with the piecewise linear nonconforming Crouzeix-Raviart finite elements. Under some assumptions on the regularity of the exact solution, the $L^2(L^2)$ and $L^2(H^1)$ error estimates are established. At the end of the paper, some computational results are presented demonstrating the application of the method to the solution of viscous gas flow.
DOI : 10.1023/A:1021701705932
Classification : 35K57, 35K60, 65M12, 65M15, 65M50, 65M60, 76M10, 76M12, 76M25, 76R99
Mots-clés : nonlinear convection-diffusion problem; compressible Navier-Stokes equations; cascade flow; barycentric finite volumes; Crouzeix-Raviart nonconforming piecewise linear finite elements; monotone finite volume scheme; discrete maximum principle; a priori estimates; error estimates 
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     author = {Dolej\v{s}{\'\i}, V{\'\i}t and Feistauer, Miloslav and Felcman, Ji\v{r}{\'\i} and Klikov\'a, Alice},
     title = {Error estimates for barycentric finite volumes combined with nonconforming finite elements applied to nonlinear convection-diffusion problems},
     journal = {Applications of Mathematics},
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Dolejší, Vít; Feistauer, Miloslav; Felcman, Jiří; Kliková, Alice. Error estimates for barycentric finite volumes combined with nonconforming finite elements applied to nonlinear convection-diffusion problems. Applications of Mathematics, Tome 47 (2002) no. 4, pp. 301-340. doi : 10.1023/A:1021701705932. https://geodesic-test.mathdoc.fr/articles/10.1023/A:1021701705932/

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